Question

Any help, I would highly appreciate it ​

Answer 1

Answer:

B

Step-by-step explanation:

We are given the equation:

$\displaystyle x(b-c) = y+x$

And that:

$2b=3c=7$

And we want to find the value of y / x.

To start, subtract x from both sides in the first equation:

$x(b-c) -x = y$

Divide both sides by x:

$\displaystyle \frac{x(b-c)-x}{x}=\frac{y}{x}$

Simplify:

$\displaystyle (b-c)-1 = \frac{y}{x}$

Next, in the second equation, divide everything by two:

$\displaystyle b = \frac{3}{2} c = \frac{7}{2}$

Substitute:

$\displaystyle \left(\frac{3}{2} c - c \right) - 1= \frac{y}{x}$

Simplify:

$\displaystyle \frac{1}{2} c - 1 = \frac{y}{x}$

From the modified second equation, we can multipy both sides by 1/3:

$\displaystyle \frac{1}{2} c = \frac{7}{6}$

Substitute:

$\displaystyle \left(\frac{7}{6}\right) -1 = \frac{y}{x}$

Subtract:

$\displaystyle \frac{y}{x} = \frac{7}{6} - \frac{6}{6} = \frac{1}{6}$

Therefore, our answer is B.